Question

1)ABC company is expecting a period of intense growth and has decided to increase its annual dividend by 10 percent a year for the next two years. After that, it will maintain a constant dividend growth of 2%. The company just paid $1.80 per share. What is the value of this stock if the required rate of return is 13 percent?

2)

XYZ company has $140,000 budget constrain on new project (it can invest only $140,000). The company is considering several projects. Project A costs $100,600 and has PV of future cash inflows of $150,750. Project B costs $39,000 and has PV of future cash inflows of $36,600. Project C costs 70,400 and has PV of future cash inflows of $75,450.

Which project or projects, if either, should the company accept based on the profitability index rule?

Answer 1

Solution:

1)

The dividend per share can be calculated as follows using MS-Excel.

Dividend per share (DPS)
Years	DPS	Increase
0	1.8	0
1	=B3+C4	=B3*0.1
2	=B4+C5	=B4*0.1
3	=B5+C6	=B5*0.02
4	=B6+C7	=B6*0.02

The result of the above table is as follows:

Dividend per share (DPS)
Years	DPS	Increase
0	$1.800	$0.000
1	$1.980	$0.180
2	$2.178	$0.198
3	$2.222	$0.044
4	$2.266	$0.044

The formula to calculate the market price of the security as on today (P0) using the variable growth rate model is as follows:

P0 = {(DPS1) / (1 + Ke)1} + {(DPS2) / (1 + Ke)2} + {(DPS3) / (1 + Ke)3} + {DPS4 / (Ke – g)} * (1 / (1 + Ke)3)

     = {(1.98) / (1 + 0.13)1} + {(2.178) / (1 + 0.13)2} + {(2.222) / (1 + 0.13)3} + {2.266 / (0.13 – 0.02)} * (1 / (1 + 0.13)3)

      = (1.98 * 0.885) + (2.178 * 0.783) + (2.222 * 0.693) + (20.60 * 0.693)

      = $19.273

Hence, the market value of the security as on today is $19.273.

P0 is the market value of the security as on today.

DPS is the dividend per share

Ke is the expected or desired rate of return of the investors.

g is the growth rate.